Find the Exact Value 2cos(15 degrees )^2-1

$2 \cos^{2} (15 °) - 1$

Apply the cosine double-angle identity.

$\cos (2 \cdot 15 °)$

Multiply $2$ by $15 °$ .

$\cos (30)$

The exact value of $\cos (30)$ is $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3}}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{2}$

Decimal Form:

$0.86602540 \dots$